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\usepackage{hyperref}
\usepackage{amsmath}
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\begin{document}
In this paper I'll compare results that we've got for Entropy for Ising model
on the triangular lattice in the transverse magnetic field with result that
Rajiv Singh got analytically using series expansion.

Parameters of the simulation:
\begin{itemize}
	\item Hamiltonian $\hat{H} = -J \sum_{\langle i j
	\rangle}\hat{\sigma_i^z}\hat{\sigma_j^z} - B \sum_i \hat{\sigma_i^x}$, where
	$\sigma$ - Pauli matrices, 
  \item Size of the lattice - $16 \times 16 $
  \item $\beta$ discretization step - $\Delta \tau =0.05$
  \item $J = 1$
  \item Number of Monte Carlo steps $10000 \tau$, where $\tau$ is correlation
  time
  \item Number of Monte Carlo steps to reach equilibrium $500 \tau$, where $\tau$ is correlation
  time
  \item $\Delta \tau$ is fixed during all simulation. Change in number of layers
  will give change in temperature. Minimum number of layers for $B \neq 0$ is 2,
  so my maximum temperature is $\frac 1 {\Delta \tau L}|_{L = 2} = 10$.
  \item Lower temperature is $0.5$. If we increase number of layers we can reach
  lower temperature, but I've limited myself to 0.5
\end{itemize}

And now - most interesting - pictures:

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B0_N16.png}}
\caption{$B = 0$}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B1_N16.png}}
\caption{$B = 1$}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B2_N16.png}}
\caption{$B = 2$}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B4_N16.png}}
\caption{$B = 4$}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B5_N16.png}}
\caption{$B = 5$}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B6_N16.png}}
\caption{$B = 6$}
\end{figure}


\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B8_N16.png}}
\caption{$B = 8$}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=100mm]{../graphs/ferromagnetic_entropy_comparison/B10_N16.png}}
\caption{$B = 10$}
\end{figure}

\end{document}